Collagen is a protein family defined by a triple helix motif, which comprises roughly one-third of the total human protein content. Decoding the reasons underlying the stability of the collagen triple helix is of both fundamental and applicative relevance, for instance, to guide collagen protein engineering. In principle, full quantum mechanical approaches based on density functional theory (DFT) are ideal to study the subtle physicochemical features of collagen. Unfortunately, the huge size of the protein prevents the straightforward application of DFT to realistic collagen protein models. In this paper, we propose a new realistic model of the collagen protein based on a periodic approach. The protein model exploits the intrinsic symmetry of the collagen triple helix, dramatically lowering the cost of the simulations. This allows using accurate hybrid DFT simulations (B3LYP-D/TZP) for systematic studies of the collagen protein features. We have tested the proposed model/level-of-theory combination to analyze the well-known proline-conformation/collagen-stability relationship. For this purpose, we have performed an extensive conformational analysis of the proline ring within the protein, clarifying some of the reasons linking specific ring conformations to helix positions. Throughout our data analysis, we have also obtained "for free" the collagen interstrand binding energy. Simulation results demonstrate that London dispersion interactions play a dominant role in the whole helix stability. The good agreement with the experimental data validates the use of the proposed model/level of theory to assist the active field of collagen-like peptide synthesis.